Blangiardo and Cameletti (2015) section 4.9
The posterior distribution of the nuisance parameter is
\[p(\psi|\mathbf{y}) \propto \frac{p(\mathbf{y} | \theta, \psi) p(\theta) p(\psi)} {p(\theta | \psi, \mathbf{y})}\]
Blangiardo, Marta, and Michela Cameletti. 2015. Spatial and Spatio-Temporal Bayesian Models with R-INLA. Wiley.
Brix, Anders, and Jesper Møller. 2001. “Space-Time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds.” Scandinavian Journal of Statistics 28 (3): 471–88.
Rue, Håvard, Sara Martino, and Nicolas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2): 319–92.